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How many even 3-digit positive integers can be formed using digits {0,

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Bunuel
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How many even 3-digit positive integers can be formed using digits {0, [#permalink] New post   28 May 2020, 02:10
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How many even 3-digit positive integers can be formed using digits {0, 1, 2, 3, 4, 5, 6}, if the repetition of the digits is allowed ?

A. 105
B. 120
C. 162
D. 168
E. 170
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D
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Re: How many even 3-digit positive integers can be formed using digits {0, [#permalink] New post   28 May 2020, 02:22
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Bunuel wrote:
How many even 3-digit positive integers can be formed using digits {0, 1, 2, 3, 4, 5, 6}, if the repetition of the digits is allowed ?

A. 105
B. 120
C. 162
D. 168
E. 170


7 digits to use are {0, 1, 2, 3, 4, 5, 6}

Repetition is ALLOWED

3 digit numbers to be made

Even Numbers to be made

Unit place can be filled in 4 ways (any of the 4 even digits 0, 2, 4, 6)

Ten's place can be filled in 7 ways (any digit from 0 to 6)

Hundred's place can be filled in 6 ways (any digit from 1 to 6)

Total Possible numbers = 4*7*6 = 168



Answer: Option D
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Re: How many even 3-digit positive integers can be formed using digits {0, [#permalink] New post   28 May 2020, 02:29
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Bunuel wrote:
How many even 3-digit positive integers can be formed using digits {0, 1, 2, 3, 4, 5, 6}, if the repetition of the digits is allowed ?

A. 105
B. 120
C. 162
D. 168
E. 170

Try similar question here: https://gmatclub.com/forum/how-many-eve ... 25375.html (repetition NOT allowed)
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Re: How many even 3-digit positive integers can be formed using digits {0, [#permalink] New post   28 May 2020, 03:53
[quote="Bunuel"]How many even 3-digit positive integers can be formed using digits {0, 1, 2, 3, 4, 5, 6}, if the repetition of the digits is allowed ?

A. 105
B. 120
C. 162
D. 168
E. 170

Last digit (0,2,4,6)
First digit can be selected in 6 ways as "0" can't be the first digit, and for second digit we have 7 ways
So total ways=6*7*4=168
D:)
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Re: How many even 3-digit positive integers can be formed using digits {0, [#permalink] New post   01 Jun 2020, 08:06
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Bunuel wrote:
How many even 3-digit positive integers can be formed using digits {0, 1, 2, 3, 4, 5, 6}, if the repetition of the digits is allowed ?

A. 105
B. 120
C. 162
D. 168
E. 170


Since 0 can’t the hundreds digit, there are 6 choices for the hundreds digit. Since the digits can be repeated and any digit can be the tens digit, there are 7 choices for the tens digit.Finally, since the number must be even, there are 4 choices (0, 2, 4, and 6) for the units digit. Therefore, the number of possible integers is:

6 x 7 x 4 = 168

Answer: D
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Re: How many even 3-digit positive integers can be formed using digits {0, [#permalink]
01 Jun 2020, 08:06
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